Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 9x - 9$ and $ BC = 6x + 3$ Find $AC$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {9x - 9} = {6x + 3}$ Solve for $x$ $ 3x = 12$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 9({4}) - 9$ $ BC = 6({4}) + 3$ $ AB = 36 - 9$ $ BC = 24 + 3$ $ AB = 27$ $ BC = 27$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {27} + {27}$ $ AC = 54$